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Figure 8.2: Noisy Add model with unlinked (X
) and linked (X
) predictors. The
model takes the same form as in
, except that the linked predictor variables
(e.g. HLA traits) have an extra hidden node. As in the univariate case (
= 1, L = 1 with probability s
. Given L
= 1, the intermediate nodes I
are 1 with probability s
A particular mutation that gives rise to an increase in ﬁtness in
a given environment and thus has become (or will become) prevalent in the
One particular gene variation.
Acquired Immunodeﬁciency Syndrome
Therapy involving any of a number of drugs de-
signed to thwart HIV infection. Major classes of antiretrovirals include drugs
that prevent the proper function of HIV Protease, Reverse Transcriptase and
Integrase, as well as drugs that interfere with HIV’s ability to fuse with certain
In the context of a conditional adaptation model, attraction de-
scribes the process whereby the presence of the predictor trait leads to mutation
toward from the amino acid described by the target trait. When an HLA allele
is the predictor trait, attraction is typically toward a speciﬁc resistant mutation.
BAYESIAN INFORMATION CRITERION:
An asymptotic approximation to the marginal
log likelihood of a model, a Bayesian measure of how well the model represents
Bayesian Information Criterion.
Broadly, any sequencing method that results in a single con-
sensus sequence for each individual.
A curve plotting (1 − Precision) against q-value.
CELLULAR IMMUNE RESPONSE:
Broadly, the part of the adaptive immune re-
sponse that is mediated by T-cells. Here, we focus on the targeting of infected
cells for destruction through HLA-1-presented epitopes.
Also known as helper T cells or eﬀector T cells, these
cells are involved in coordinating the immune response. Importantly, these are
the cells preferentially targeted by HIV.
A class of T-cells, including CTL, that express CD8.
These cells are typically involved in the direct or indirect killing of infected
HIV-1 group M (the predominant group) is divided into nine distinct
subtypes, or clades. These clades can be easily identiﬁed by building a phylogeny
from a large sample of group M sequences. Each major cluster in the tree is a
clade. In this work, we consider sequences from clade B (the predominant clade
in North American infections) and clade C (the predominant clade in South
Although codon is more precisely deﬁned to be the sequence of three
RNA bases that encode an amino acid, here we will often use the term to refer
to a position in the protein. For example, codon 3 is the 3rd position.
An association between two HIV codons. Through-
out this work, codon-codon association will typically refer to the strongest as-
sociation between a any amino acid at either of the two codons.
Broadly, any process by which two or more traits have evolved
together along the same phylogeny, each trait mutually inﬂuencing the other.
Broadly, an approach that seeks to identify the adap-
tive function of a trait by comparing the presence of that trait in diﬀerent
populations or species.
Mutation A is compensatory with respect to muta-
tion B if mutation B induces a ﬁtness cost that is relieved by mutation A.
CONDITIONAL ADAPTATION MODEL:
A probabilistic model we propose for the
PDN. In this model, the target trait is assumed to have evolved independently
throughout evolutionary time until it reaches the environment in which we are
able to observe it. In this environment, a model of selection pressure in con-
structed and the target trait is allowed to adapt to this selection pressure.
Cells that recognize HLA-I-presented epitopes and
cause the death of infected cells.
Directed Acyclic Graphical model.
DECISION TREE MODEL:
A multivariate conditional adaptation model in which
the selection pressure derived from a set of predictor traits is computed using
a Decision Tree, which is a compact way of describing the unique selection
pressure that arises from every possible conﬁguration of predictor traits. See
A probabilistic graphical model. The structure of the
model consists of nodes and directed arcs, such that the arc A → B denotes
that B is statistically dependent on A. The probability component of the model
is a set of local conditional probabilities, one for each node, that describes the
probability distribution for each node conditioned on all other nodes that point
to it in the graph.
DIRECTED ACYCLIC GRAPHICAL MODEL:
A graphical model similar to the DN,
except that directed cycles are not allowed and the goal of the model is to
maximize the joint likelihood over all the nodes in the graph.
If the inferred dependency network includes the chain A →
B → C, then A → B and B → C are direct associations. In some contexts,
direct association refers to directly interacting traits in the true causal chain.
See Precision-Recall curve.
see interferon-γ ELISpot assay.
Broadly, the part of a molecule that is the target of an immune response.
In the case of antibodies, an epitope is a region of exposed viral protein. In the
case of the cellular immune response, and epitope is a linear fragment of HIV
protein that is presented by HLA class I or class II molecules.
See immune escape for a general deﬁnition. In the context of a condi-
tional adaptation model, escape describes the process whereby the presence of
the predictor trait leads to mutation away from the amino acid described by
the target trait.
False Discovery Rate.
FALSE DISCOVERY RATE:
The expected proportion of tests called signiﬁcant that
are truly null.
Fisher’s exact test.
FISHER’S EXACT TEST:
A standard test of independence between two binary traits.
Assume each trait is IID.
Roughly, the reproductive capacity of a speciﬁc virion. Virions that are
more ﬁt will reproduce more rapidly; thus, their genetic material will come ot
dominate the population. Fitness can be estimated in vitro using, for example,
viral replication or competition assays. Selection pressure changes which virions
are more ﬁt than others, and the speciﬁc mutations that increase ﬁtness are
An mutation is said to be ﬁxed in a population when the vast majority
of individuals have the mutation.
FOLLOW THE TREE:
A trait is said to follow the tree or phylogeny if that phy-
logeny (approximately) describes the evolutionary history of that trait.
An HIV polyprotein involved with the structure of the virion. Upon mat-
uration, the Gag protein is cleaved into several smaller proteins, including p17
(Capsid) and p24 (Matrix), which we look at in
. CTL response against
Gag have been weakly correlated with control of viremia [
Genome Wide Association Study.
GENOME WIDE ASSOCIATION STUDY:
An approach to identifying genetic varia-
tions that cause speciﬁc phenotypes by comparing a large set of SNPs to phe-
notypes in a large number of individuals.
Human Leukocyte Antigen.
An association between an HLA allele and an HIV
codon. Throughout this work, HLA-codon association will typically refer to the
strongest association between a given HLA allele and any amino acid at that
HLA class I.
HUMAN LEUKOCYTE ANTIGEN:
The human major histocompatibility complex pro-
teins. There are two classes, I and II. In this work, we focus on class I, which
are primarily responsible for presenting viral epitopes on the surface of infected
cells. Among class I, there are three loci: A, B and C. Thus, each individual
has six HLA genes (three from each parent).
In this document, shorthand for HIV-1.
Human Immunodeﬁciency Virus Type 1. The lentivirus (a member of the
retrovirus family) that causes AIDS.
Independent and identically distributed.
An immune escape mutation is an adaptation that reduces the
ability of an individual’s immune system to target HIV.
An epitope is immunodominant if it elicits a strong CTL
response. It is subdominant if it elicits a weak response. The immunodominance
hierarchy can refer either to the relative strength of epitope targeting at a given
time point, or can refer to the progression of which epitopes are immunodom-
inant throughout the course of infection. Patterns of immunodominance are
largely consistent in similar patients, though there appears to be a considerable
amount of randomness as well.
The (incompletely understood) process by why the CTL
response actively keeps some epitopes subdominant while others are maintained
INDEPENDENT AND IDENTICALLY DISTRIBUTED:
A collection of random variables
is independent and identically distributed if each random variable has the same
probability distribution and all random variables are statistically independent
of the others.
If the inferred dependency network includes the chain
A → B → C, then A → C is an indirect association. In some contexts, indirect
association refers to indirectly interacting traits in the true causal chain.
INTERFERON-γ ELISPOT ASSAY:
Measures the number of cells secreting interferon-
γ in under certain conditions. In this work, ELISpot speciﬁcally refers to tests
designed determine whether a patient’s immune system can target an epitope.
This is done by incubating patient-derived cells with the epitope, then test-
ing for the secretion of interferon-γ, which indicates the active targeting of the
epitope by CTL.
The speciﬁc probability distribution of a conditional adap-
tation model that describes the probability of a given adaptation in response to
Two genetic traits are in linkage disequilibrium if they
tend to be inherited together, such that two random variables represented the
two traits cannot be considered independent. In this work, the linkage disequi-
librium among HLA alleles is considered.
The probability of the data given a speciﬁc model.
LIKELIHOOD RATIO TEST:
A method for comparing two models, by which the
maximum likelihood of model A is divided by the maximum likelihood of model
B. If B is a special case of A (typically, B represents a null model that is
a simpliﬁed version of A), then the ratio of the likelihoods is χ
allowing us to compute a p-value analytically.
Likelihood Ratio Test.
The maximum likelihood over all possibly parameteriza-
tions of a model.
MULTIVARIATE CONDITIONAL ADAPTATION MODEL:
Generally, a conditional adap-
tation model in which there are more than one predictor variables.
Typically refers to a spontaneous change in genomic DNA (RNA in
the case of HIV). In this document, mutation is often used as a synonym for an
amino acid substitution, as we are primarily interested in mutations that lead
to amino acid substitutions.
The process by which deleterious mutations are removed
from the population due to their negative impact on ﬁtness. In the context of
Noisy Add, negative selection refers to pressure to move away from the amino
acid (assuming by analogy that the amino acid is deleterious).
If in a given position no mutation is favored by selection
pressure, then neutral evolution describes the process whereby the frequency of
each mutation in the population follows a random walk.
NOISY ADD MODEL:
A multivariate conditional adaptation model in which selec-
tion pressure is modeled as a stochastic, additive process from a set of predictor
traits, each of which my contribute positive or negative selection pressure on
the target trait.
A mutation in DNA/RNA that leads to an amino
Phylogenetic Dependency Network.
Positive False Discovery Rate.
Any non-genetic, observable trait.
PHYLOGENETIC DEPENDENCY NETWORK:
A dependency network in which the
local conditional probability component for each node is conditioned on the
phylogeny using a model of evolution.
A tree structure that deﬁnes the ancestor-descendent relationships
of a group of species or populations.
PLASMA VIRAL LOAD:
The quantity of virus per milliliter of plasma.
The HIV polyprotein that is cleaved into Protease, Reverse Transcriptase,
A speciﬁc genetic variation at a speciﬁc site. We refer to poly-
morphisms both at the DNA/RNA level and at the protein level.
POSITIVE FALSE DISCOVERY RATE:
The FDR conditioned on the rejection of at
least one test.
The process by which an adaptation moves to ﬁxation in
the population. In the context of Noisy Add, positive selection refers to selective
pressure that favors the amino acid.
The proportion of tests called signiﬁcant that are true alternative
tests (i.e., associations that are in fact “real”).
A curve that plots precision against recall for a group
of methods. The curve for a given method is constructed by ordering all of the
predictions of that method by q-value. The precision and recall are calculated
for each q-value threshold and the resulting curve is plotted.
In the context of a PDN, the predictor trait is any node on
which a target trait is conditioned.
A synonym for negative selection.
A measure of statistical signiﬁcance. Roughly, the probability of seem-
ing something at least this signiﬁcant under the null hypothesis.
Plasma Viral Load.
The FDR analogue of the p-value. The q-value of a test is the minimum
FDR for any signiﬁcance threshold that would cause this test to be rejected.
The distinct population of HIV virions infecting a single patient.
Due to the rapid rate of mutation and adaptation in HIV, the HIV population
infecting each patient is typically quite diﬀerent from that infecting any other
The proportion of true alternative tests (i.e., associations that are “real”)
that are called signiﬁcant.
In the context of a conditional adaptation model, repulsion describes
the process whereby the absence of the predictor trait leads to mutation away
from the amino acid described by the target trait.
In the context of HLA-codon associations, the resistant form
is that correlated with the presence of the HLA, and thus presumed to provide
relative resistance against HLA-mediated epitope targeting.
Reversion occurs when a codon mutates back to the susceptible fol-
lowing the removal of the selection pressure. It is, in eﬀect, an adaptation that
undoes a previous adaptation, and typically occurs when the escape adaptation
incurs a ﬁtness cost on the virus. In this case, when the virus is transmitted
to an HLA-mismatched recipient, the selection pressure favoring the adaptation
is removed, and the adaptation is actively selected against due to the ﬁtness
cost. In the context of a conditional adaptation model, reversion describes the
process whereby the absence of the predictor trait leads to mutation toward the
amino acid described by the target trait.
Any environmental trait that reduces the ﬁtness of some
mutations and favors the ﬁtness of other mutations is said to exert selection
Single Genome Sequencing.
SINGLE GENOME SEQUENCING:
Broadly, any method by which single virion se-
quences are obtained.
Simian Immunodeﬁciency Virus. An HIV-like virus that infects some species
of monkeys. HIV is believed to have arisen from SIV around the turn of the
20th century [
Single Nucleotide Polymorphism.
SINGLE NUCLEOTIDE POLYMORPHISM:
A genetic variation or mutation that oc-
curs at a single position.
In the context of HLA-codon associations, the susceptible
form is that correlated with the absence of the HLA, and thus presumed to be
susceptible to HLA-mediated epitope targeting.
A mutation in DNA/RNA that does not lead to an
amino acid change.
In the context of a PDN, the target trait refers to the node for
which we are currently deﬁning the local conditional probability distribution.
A certain characteristic of an individual, population or environment. In
this work, typical traits include whether or not a patient has a given HLA allele,
and the speciﬁc amino acid observed at a speciﬁc position in an HIV protein.
UNIVARIATE CONDITIONAL ADAPTATION MODEL:
A speciﬁc conditional adapta-
tion model in which there is only one predictor trait.
In the context of a PDN, a variable is shorthand for a random variable
that represents a given trait for a given individual. For example, Y
is a random
variable for trait Y in individual i.
See plasma viral load.
The presence of virus in the bloodstream.
An individual virus particle.
 Addo MM, Yu XG, Rathod A, Cohen D, Eldridge RL, Strick D, Johnston
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